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I can't disable the "An administrator must always approve the comment" option!

This is intentional... it is how we funnel all comments into the Comment Inbox. Ignore the wording. All non-spam comments appear on the blog immediately.

How do I stop all the "you have a comment awaiting moderation" e-mails?

Go to Options/Settings > Discussion and uncheck the "[E-mail me whenever...] A comment is held for moderation" box.